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My scenario is casting a WC3 spell with 7dice.

I have found the charts that tell me what the percentages are, and I can find out what the percent chance of succeeding would be if I drew a tree diagram, but I was wondering is there an easier way to express this mathematically?

Finding a success of a WC3 spell with 3 dice is simple but I lose track when it gets to rolling three 4+'s on four dice. I can count the outcomes from four dice and give a fraction (5/16) but that becomes quite cumbersome at seven dice. Could someone with a better understanding of probability help me out? Thanks!]]> http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694784.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694784.page GMT http://www.torrentoffire.com/4776/the-math-of-the-new-psychic-phase]]> http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694830.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694830.page GMT http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694922.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8694922.page GMT http://stattrek.com/online-calculator/binomial.aspx]]> http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8695087.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8695087.page GMT
WC1 power succeeds 50% of the time with 1 die.
WC2 power succeeds 50% of the time with 3 dice
WC3 power succeeds 50% of the time with 5 dice.

After that, each additional dice gets you 1/(WC+1)% of the way towards 100%. It's not perfectly accurate (actually, it is with WC1 powers), but it's close enough for mental stuff. So, without checking, if 5 dice on WC3 nets a 50% return, 6 dice gives you just about a 65% chance, and 7 dice would be about 75%. Checking the calculator, I see that I'm only off by about 2%.]]> http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8695330.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8695330.page GMT http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8709556.page http://www.dakkadakka.com/dakkaforum/posts/preList/692858/8709556.page GMT